Regardless the fitting software and your particular samples which I never have a chance to work on, here is my answers to your questions based on my own experience to deal with the multilayer or any kind of XR fitting for thin film sample:

1. Always try to get a good thickness matching first by fitting your calc curves with the oscillation frequency of the exp. curves.

2. In any case, before measuring XR, you should be aware of the structure of your sample, how its composed and how layer structures are constructed in the direction normalized to the interface.

3. You should have some approximated value of electron density and thickness of each layer. Of course, the fitting values are usually deviated from the theoretical/calculated values (usually lower for electron density in my cases).

4. In case you do not know which layer thickness influence which particular region of the ref. curve, the reflectivity data is actually the Fourier transform of the total reflectivity from all layers. Therefore, one suggestion is that you may want to do simulation for each layer with approximately same estimated thickness to see how the curve looks like, then combining each pair of two curves adjacent each other, then three, four, and so on. 

It sounds complicated and does require time and effort to accumulate experience when you deal with fitting of multilayers.

One clear example, not multilayer (sorry) but its suited your question:

I used to work on brush polymer deposited on gold substrate. Gold is approximately 50nm, while polymer is thermal responsive polymer and the thickness is ranged from 15 to 25nm. However, 'coz Au has too high ED compared to polymer, the oscillations from the XR curves are mainly originated from the Au layer, no matter how much I changed (in a logical range) the thickness of the polymer. In this case, the oscillations from the region before critical angle is actually originated from polymer and helped me solve problem. Of course, I realized that by simulation after measurement (my fault), and I had to measure all over again to get the right number of counts for that region. For this example, of course I wish I could measure by neutron reflectivity instead of x-ray, but my collaboration could not prepare the sample with that huge substrate area.

Hope it helps. Minh Phan.

Thank you for the answer Mr. Minh Phan,

Your answer was indeed helpful to me. However, I have a few more queries. 

1. In our fitting software we can vary the rho value and imaginary rho value apart from the layer thickness and roughness value. But these values are meant to be constant for a particular material and were obtained from the CXRO database. I am not sure whether we are allowed to include these parameters while performing the iteration?

2. Also, there are some variables corresponding to the rh and, img. rho values for air and the bulk/substrate material. Please suggest me whether we are allowed to include these parameters for the iteration and if yest to what extend we can vary these terms?

3. As you mentioned I will perform the simulation for individual layers. Is it okay to take the same thickness as in our case which is very small (~ 1-3 nm) while simulating ?

Thanks and warm regards

1. Is "rho value" the electron density of sample? Typically, X-ray interacts with electron, and for X-ray reflectivity, I would only concern about three essential parameters: thickness, electron density and roughness. And yes, I usually get the electron dispersion (delta value in refractive index equation) from CXRO database as well, but usually I put those values a bit lower in my fitting than the reference. Electron dispersion is a real part of index of refraction and is obtained from the fitting, and is linearly proportional to the electron density.

2. The parameters for bulk and substrate should be constant as same as the theoretical reference, and you only play around with the experimental compartments. For example, if your substrate is silicon wafer in liquid, and you oxidize the substrate to deposit some hydrophilic samples on. Then in the fitting, you should not touch the parameters identified the media (liquid) and bare substrate (Si wafer), but rather playing with oxide layer and your sample. Of course the roughness of substrate can be varied in the interation, but should be a final concern after all parameters of samples are well-fitted to the exp. curves.

3. The purpose of simulation is to understand visually how each layer and the combination of layers could contribute to the final data. Therefore, the two parameters which you can mainly play are electron density and thickness. Anyway, the simulation routine I am saying here is not standard, but rather from my own experience. The more standard way, as I have been trained, to understand the exp. data and where the fitting should go, should be from physics understanding of interference of waves and scattering principle.

rho is the real part of the Scattering Length Density. It is a measure of the scattering power of a material. It increases with the physical density (how tightly packed the scattering entities are), as well as the intrinsic scattering power of the 'scattering entities'. For x-rays, the scattering arises from the electron density.

As I answered above, you only need to fix rho and imaginary rho for media and substrate. The rest of layers constructing your sample can be varied to get the best fit.

By the way, I would rather name the value, instead of its symbol, because in fact many books and articles use different symbols for the same meaning. As I understand from your explanation, rho is electron dispersion and imaginary rho is probably electron adsorption. These two values contribute two parts of refractive index. Depending on sample, the ratio between electron dispersion/electron adsorption is more or less important. 

Hope it helps. Minh Phan.

Thankyou very much Mr. Minh Phan. Your suggestions helped me a lot.

Thanks and Regards.  Murali Krishnan